The aim of the present paper is to de…ne and study the notion of quasi bi-slant submanifolds of almost contact metric manifolds. We mainly concerned with quasi bi-slant submanifolds of cosymplectic manifolds as a generalization of slant, semi-slant, hemi-slant, bi-slant and quasi hemi-slant submanifolds. First, we give non-trivial examples in order to demostrate the method presented in this paper is e¤ective and investigate the geometry of distributions. Moreover, We study these types of submanifolds with parallel canonical structures.
The objective of this paper to introduce a new class of sub- manifolds
which are called pointwise quasi hemi-slant submanifolds in almost
Hermitian manifolds which extends quasi hemi-slant, hemi-slant,
semi-slant and slant submanifolds in a very natural way. Several basic
results in this respect are proved in this paper. Moreover, we obtain
some conditions of the distributions which are involved in the denition
of the new submanifolds. We also get some results for totally geodesic
and mixed totally geodesic conditions for pointwise quasi hemi-slant
submanifolds. Finally, we illustrate some examples in order to garanty
the new kind of submanifolds.
This study is concerned with some results on generalized weakly symmetric and generalized weakly Ricci-symmetric α-cosymplectic manifolds. We prove the necessary and sufficient conditions for an α-cosymplectic manifold to be generalized weakly symmetric and generalized weakly Ricci-symmetric. On the basis of these results, we give one proper example of generalized weakly symmetric α-cosymplectic manifolds.
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